Last December, as the world reeled from the deadly attacks in Paris and San Bernardino, California, President Barack Obama fully backed lawmakers who passed legislation aimed at keeping out terrorists who try to reach the U.S. through the popular Visa Waiver Program.

But nearly four months after Obama signed the bill into law, his administration is struggling to implement a key piece of it, one that affects dual nationals. It also is refusing to release clear criteria as to how it will apply that part of law.

That is frustrating both critics and supporters of the measure who worry the new screening process is at best confusing, at worst discriminatory and ultimately ineffective at catching would-be enemies of the United States. One senior Department of Homeland Security official, in describing the challenges involved in enforcing the law, called the new set-up “an honor system with checks and balances.”

The administration’s grappling comes as the European Union prepares to consider Tuesday whether to require all American travelers to obtain visas — the latest in an escalating spat over travel deals between Washington and Brussels. It also comes as a leading opponent of the dual national provision, Sen. Jeff Flake, is trying to get it repealed through an amendment to the Federal Aviation Administration re-authorization bill this week.

I don’t think they fully thought through what the response would be from Europe and the number of people that would be caught up without any gains in national security — Sen. Jeff Flake

“We need this fixed, and I hope the administration will help us out,” the Arizona Republican said. As for the people who supported it? “I don’t think that they understood the way nationality, dual nationality, is conferred by some countries,” Flake said. “I don’t think they fully thought through what the response would be from Europe and the number of people that would be caught up without any gains in national security.”

The new U.S. law — passed as part of the omnibus spending bill — made significant changes to the Visa Waiver Program, which allows citizens of 38 mostly European countries to temporarily visit the U.S. without a visa. The dual national provision requires citizens of those countries to get visas if they also happen to be nationals of Iran, Iraq, Syria or Sudan.

Civil liberties and minority rights groups pointed out that there is no international agreement on the rules of nationality and that many people are dual nationals even if they do not wish to be. They warned that the law was a form of ethnic and ancestral discrimination because some countries treat nationality as something passed down from father to child.

So a woman born and raised in Japan (one of the 38 countries) is considered Iranian under Iranian law if her father is Iranian — even if she has never visited the Middle Eastern state. Nationality also can be conferred through marriage, according to some interpretations of Iranian law. And such nationality is rarely easy to renounce — and just because a person obtains foreign citizenship doesn’t mean they are no longer Iranian, Iraqi, Sudanese or Syrian.

POLITICO has been asking the administration since December to lay out how it will decide who qualifies as a citizen of Syria, Iraq, Sudan or Iran, a determination that could set an international precedent. In a statement to POLITICO late last week, officials indicated the strategy will be to determine each potential visitor’s nationality on a case-by-case basis.

“The U.S. government need not recognize another country’s conferral of nationality if it determines that nationality to be ‘nominal,’ or, in other words, if the connections indicating potential nationality are so minimal or attenuated that an individual should not be considered a dual national for the purposes of the U.S. Visa Waiver Program,” the DHS statement says. “In this way, DHS assesses whether an individual is a national of a country based on an individual’s relationship to that country, such as if an individual maintains allegiance to that country.”

But administration officials declined to answer specific questions posed by POLITICO, such as whether they will consider children born to Iranian fathers outside Iran as Iranian, whether they will count only people born in one of the four countries as nationals of those countries, or whether they will consider nationality conferred through marriage as valid. They also would not specify what counts as “maintains allegiance.”

A senior U.S. government official said the decision not to lay out clear rules is “being done out of an abundance of caution in order to prevent any potential malevolent actors from gaming the system.”

That didn’t pass muster with even some supporters of the dual national provision, who say the administration’s approach is problematic and could lead to inconsistent application of the law.

Emanuele Ottolenghi, a senior fellow at the Foundation for Defense of Democracies, said he worries terrorists from those four countries — but especially Iran — can currently easily exploit lax travel restrictions to get their operatives to the United States. But he said not laying out the official guidelines for who the U.S. will consider a dual national could render the new system worthless.

“The risk that people lie always exists — and if this is what DHS truly fears, then they should discard the Visa Waiver Program altogether. To not disclose clear criteria for fear that people might try to cheat the system will in fact produce the opposite outcome,” he warned.

Already, the changes to the visa waiver law have snared European journalists, artists and academics who were used to visiting the U.S. without a visa and suddenly found themselves required to get one.

“By failing to provide clarity in how the restrictions will be enforced, it further feeds people’s perception that they are being discriminated against and that they face increased risk of travel restrictions because of their family heritage,” said Jamal Abdi of NIAC Action, an Iranian-American activist group.

The way the U.S. captures information about potential visitors is through the Electronic System for Travel Authorization form. Visitors from the 38 countries must fill out an ESTA form before coming to the United States. If the authorization comes through, no visa is needed. If it doesn’t, a person has to set up an appointment with the U.S. embassy or consulate to obtain a visa, an often time-consuming and expensive process.

But the ESTA forms themselves are confusing. Two of the early questions ask if an applicant is or has ever been a citizen or national of another country; the only answer options are “yes” or “no.” For potential dual nationals who don’t know what standards the U.S. is applying, it’s unclear which answer to pick.

For those who say they are dual nationals of Iran, Iraq, Syria or Sudan, follow-up questions ask how that person acquired that country’s nationality. Anyone who lists their birthplace as Iran, Iraq, Syria or Sudan is likely to get follow-up questions as well. But unless a person is familiar with the (often unclear) nationality laws of various countries in play, they may not know the proper answers.

“DHS is asking people who want to use the visa waiver program if they are a national or citizen of one of those countries, which many applicants will feel uncomfortable answering because it puts them in the position of making a complex legal determination,” said Greg Chen, director of advocacy at the American Immigration Lawyers Association.

The senior DHS official acknowledged that the way the form is set up, some ill-intentioned people who technically are dual nationals could still get to the U.S. without a visa. For example, if someone wasn’t born in Iran, Iraq, Syria or Sudan and has never obtained a travel document or passport for those countries, they may not get flagged.

But he also noted that the U.S. has other safeguards in place as part of the process, including human review and checking terror watch-lists, that could prevent abuses.

“The way we’re approaching this is to try to make sure we’re not over-inclusive in imputing dual national status to someone who may have only limited links to the countries in question,” the official said. “It’s an honor system with checks and balances.”

The European Union was one of the early critics of the new U.S. visa rules, but it also has long been frustrated that the U.S. does not allow five EU countries (Croatia, Poland, Bulgaria, Cyprus, and Romania) to be part of the Visa Waiver Program in the first place.

On Tuesday, the bloc’s executive body will review the program, and it has floated the idea that it might halt visa-free travel for Americans heading to Europe to pressure the U.S. Although the EU is unlikely to take such a drastic step because of the business and tourism fallout, the fact that it’s under discussion shows how ugly the dispute has gotten.

The new U.S. visa rules also require would-be visitors from the 38 countries to get a visa if they have traveled to Syria, Iraq, Sudan and Iran since March 2011. But the administration has carved out exceptions for journalists, aid workers and others, although it has also not been clear as to how it will define those groups.

While strong legislative support exists for the travel provisions, a growing number of lawmakers are unhappy with the effects on dual nationals. Among the lawmakers willing to rethink the dual national element is Rep. Candice Miller, lead sponsor of the original bill.

“I understand that issues have been raised with the dual national provision and believe that those concerns may warrant additional discussions,” Miller, a Michigan Republican, told POLITICO in a statement.